1

Rendezvous Design Algorithms for Wireless Sensor Networks with

a Mobile Station

Guoliang Xing; Tian Wang; Weijia Jia; Minming Li

Department of Computer Science City University of Hong Kong

2

Outline

• Motivation

• Problem formulation

• Rendezvous design algorithms– Free mobility model– Limited mobility model

• Simulations

• Conclusion

3

Challenges for Data-intensive Sensing Applications

• Many applications are data-intensive – Structural health monitoring

• Accelerometer@100Hz, 30 min/day, 80Gb/year

– Micro-climate and habitat monitoring• Acoustic & video, 10 min/day, 1Gb/year

• Most sensor nodes are powered by batteries• A tension exists between the sheer amount of

data generated and the limited power supply

4

Mobility-assisted Data Collection

• Mobile nodes collect data via short-range communications

• Mobile nodes are less power-constrained– Can move to wired power sources

Base Station

500K bytes

100K bytes 100K bytes

150K bytes5 m

ins

10 mins5 mins

5

Mobile Sensor Platforms

• Low movement speed (0.1~2 m/s)– Increased latency of data collection– Reduced network capacity

Networked Infomechanical Systems (NIMS) @ CENS, UCLA

Robomote @ USC [Dantu05robomote]

XYZ @ Yale http://www.eng.yale.edu/

enalab/XYZ/

6

Static vs. Mobile

All-static networks

Mobility-assisted Networks

Delay Low High

Energy Consumption

High nonreplenishable

High

replenishable

Bandwidth Medium Medium to high

7

Rendezvous-based Data Collection

• Some nodes serve as “rendezvous points” (RPs)– Other nodes send their data to the closest RP– Mobiles visit RPs and transport data to base station

• Advantages – In-network caching + controlled mobility– Mobiles can collect a large volume of data at a time– Minimize disruptions due to mobility

• Mobiles contact static nodes at RPs at scheduled time

8

mobile node

rendezvous point

Rendezvous-based Data Collection

source node

• Some nodes serve as “rendezvous points” (RPs)– Others nodes send data to

the closest RP– Mobiles visit RPs and carry

data to base station

• Advantages – In-network caching +

controlled mobility– Minimize disruptions due to

mobility

9

Outline

• Motivation

• Problem formulation

• Rendezvous design algorithms– Free mobility model– Limited mobility model

• Simulations

• Conclusion

10

The Rendezvous Design Problem

• Choose RPs s.t. mobile nodes can visit all RPs within data collection deadline

• Total network energy of transmitting data from sources to RPs is minimized

• Joint optimization of positions of RPs, mobile motion paths, and data routes

11

Assumptions

• Only one mobile, moves at speed v

• Mobile picks up data at locations of nodes

• Data from two sources can be aggregated

• Data collection deadline is D– User requirement: “report every 10 minutes and

the data is sampled every 10 seconds”– Recharging period: e.g., Robomotes powered

by 2 AA batteries recharge every ~30 minutes

12

Geometric Network Model• Transmission energy is proportional to distance• Base station, source nodes and RPs are

connected by straight lines

a multi-hop route is approximated by a straight line

source nodes

Source nodes

approximated data route

real data route

Non-source nodes

Rendezvous points

13

The Rendezvous Design Problem

Given a base station B, and sources

{ si }, find trees Ti( Vi, Ei ), and a tour

visiting the roots of Ti such that

1) the tour is no longer than L;

2) the total edge length of Ti is minimized

R1s1

s5

s4

B

s2s3

R2

R3

R4

s6

Hardness• General case is NP-Hard •When L=0, the opt solution is Steiner Min Tree that connects {B} U { si }

14

Outline

• Motivation

• Problem formulation

• Rendezvous design algorithms– Free mobility model– Limited mobility model

• Simulations

• Conclusion

15

An Approx. Algorithm

• Find an approx. Steiner Min Tree for

{ B }U{ si }

• Depth-first traverses the tree until covers L/2 edge length

16

An Improved Algorithm

1. Find T -- an approx. SMT for { B }U{ si }

2. Y=L/2;

3. Depth-first traverses T from B until cover Y length, denote I as the set of current RPs

4. if X = L − TSP(I) > δ Y=Y+X/2; goto 3;

else exit;

TSP(I) – the length of tour visiting points in set I, computed by a Traveling Salesman Problem solver

17

Illustration1. Find T - an approx. Steiner min

tree of {B}U{si}

2. Y=L/2;

3. Depth-first traverse T from B until cover Y length, denote I as the set of border points

4. if X = L − TSP(I) > δ Y=Y+X/2; goto 3;

else exit;

18

Approx. Ratio

• The approximation ratio of the algorithm is α+β(2α-1)/2(1-β)

– α is the best approximation ratio of the Steiner Minimum Tree problem

– β = L / SMT(BS + Sources)

– Assume L << SMT(BS + Sources)

19

Outline

• Motivation

• Problem formulation

• Rendezvous design algorithms– Free mobility model– Limited mobility model

• Simulations

• Conclusion

20

Illustration

• The mobile only moves along a fixed track

Track of Mobile

XYZ node @ Yale

source node

rendezvous point

21

Theoretical Results

• An MST-based approximation algorithm

• Approximation ratio is 2(1+3 β)/sqrt(3)– β = ∆L/c(MSTopt) – ∆L is a user-specified constant– c(MSTopt) is cost of the optimal Min Spanning

Tree connecting sources to the track

22

Simulation Results

• 100 sources are randomly distributed in a 300m X 300m field, base station is on the left corner

• Each source generates 2 bytes/s, deadline is 20 mins

23

Conclusions

• Rendezvous-based data collection for WSNs w/ a mobile base station– In-network caching + controlled mobility– Problem formulations under both free/limited

mobility models

• Two graph-theoretical rendezvous algos– Provable performance bounds– Simulation-based evaluation

24

Geometric Network Model• Transmission energy is proportional to distance• Base station, source nodes and branch nodes

are connected with straight lines

a multi-hop route is approximated by a straight line

Source nodes

Source nodes

approximated data route

real data route

Non-source nodes

Branch nodes

Rendezvous points

a branch node lies on two or more source-to-root routes

25

Problem Formulation

• Given a tree T(V,E) rooted at B and sources {si}, find RPs, {Ri}, and a tour no longer than L=vD that visits {B}U{Ri}, and

• The problem is NP-hard (reduction from the Traveling Salesman Problem)

minimized is ),( isS

iiT Rsd

dT(si,Ri) – the on-tree distance between si and Ri

26

Illustration of Problem Formulation

Objective– Minimize edge length

of routing tree

Constraint – Tour length ≤ L

Source nodes

Rendezvous points data route

branch nodes

27

Proof Sketch I• A* is opt solution

• R={B} U {Ri}

• S={B} U {Si}• T is the tree used in input• SMT(X) - SMT connecting

points in set X• TSP*(X) - length of the shortest

tour visiting points in R

R1

R2

R3

B

28

Proof Sketch II

R1

R2

R3

BA* U SMT(R) is a Steiner tree connecting S:c(A*) + c(SMT(R)) ≥ c(SMT(S))

SMT is a lower bound of TSP problem:c(SMT(R)) < c(TSP*(R)) ≤ L

c(A*) > c(SMT(S)) – L > c(T)/ α - L

Our solution = c(T)-L/2

S1

S2

S3

S4

S5